I live in the USA. Oh, you mean the same ER that will slap you with a several thousand dollar invoice (only after the services are provided, of course) after a 3 hour wait? Well that's a related but different story I won't get into at this time.
If I have have an infected tear duct (in fact, I do) requiring a visit to an ENT specialist (for example), it's frankly absurd that the next appointment requires a 2-6 week wait. And then it also affects the work day because ENTs docs are only available 9-5.
Why aren't there two shifts of doctors: 7am - 3pm, and (as an example) 12pm-8pm? At least I work a computer-based job; what about a construction worker or other blue-collar worker who has to take an entire day off because they can't log in and continue work remotely (and if you know blue collar folks, this is the reason many will skip preventative care until they are critically ill)?
Your argument seems to be "well you won't lose the eye or go blind so it's fine" and that simply isn't how we should be viewing healthcare.
And just for posterity's sake, I've spent years at hospitals and medical device companies, my background is in biomedical engineering, and I'm not what you'd consider a layman in this area.